The digital structural analysis of cadmium selenide crystals by a method of ion beam thinning for high resolution electron microscopy

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rnGreatBrit~in Acta, Vol. 17, No. 1, pp. 25-43, 1986.

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THE DIGITAL STRUCTURAL ANALYSIS OF CADMIUM SELENIDE CRYSTALS BY A METHOD OF ION BEAM THINNING FOR HIGH RESOLUTION ELECTRON MICROSCOPY Koicm KANAYA,* NoRlo BABA,* MICHIAKI NAKA,* YuKIHIsA KITAGAWA5 and KUNIO SUZUKIt *Kogakuin University, Nishishinjuku, Shinjuku-ku, Tokyo, Japan and tlnstitute for Solid State Physics, University of Tokyo, Roppongi, Minato-ku, Tokyo, Japan (Received 19 April 1985; revised 29 August 1985)

Abstract—A digital processing method using a scanning densitometer system for structural analysis ofelectron micrographs was successfully applied to a study of cadmium selenide crystals, which were prepared by an argon-ion beam thinning method. Based on Fourier techniques for structural analysis from a computer-generated diffractogram, it was demonstrated that when cadmium selenide crystals were sufficiently thin to display the higher order diffraction spots at a high resolution approaching the atomic level, they constitute an alternative hexagonal lattice of imperfect wurtzite phase from a superposition of individual harmonic images by the enhanced scattering amplitude and corrected phase. From the structural analysisdata, a Fourier synthetic lattice image was reconstructed, representing the precise location and three-dimensional arrangement of each ofthe atoms in the unit cell. Extensively enhanced lattice defect images of dislocations and stacking faults were also derived and shown graphically. Index key words: Digital processing, Fourier transform, computer-generated diffractogram, computergenerated lattice image, dislocation, stacking fault, ion beam thinning.

cadmium sulphide (Cockayne et al., 1980), and stacking faults in vapour-deposited poiycrystalline cadmium suiphide (Norian and Edington, 1981) have been observed previously. However, the structural details were not investigated. Structural details ofa 60°dislocation, stacking faults and partial dislocations have been revealed with the aid of high-resolution electron microscopy at an atomic level, where specimens were prepared with the aid of an argon-ion beam thinning method described by Echigoya et a!. (1982). Similarly, some preliminary results showing various lattice defects, dislocations and stacking faults by plastic deformation after ion bombardment were reported from studies of CdSe single crystals by Suzuki et a!. (1982, 1983). However, the precise location and three-dimensional arrangement of each atom within the wurtzite structure was not established. In the present paper the digital structural analysis method previously described by Kanaya

INTRODUCTION Following the demonstration that lattice images of (20T) (1.2 nm spacing) could be resolved in platinum phthalocyanine crystals by Menter (1956, 1960), high resolution electron microscopy has become one ofthe most powerful tools for the direct identification of crystal lattice defects. Many calculations concerning the diffraction contrast from various crystal defects have subsequently been performed as shown in the publications of Hirsch et a!. (1965), Murr (1970), Vainshtein et a!. (1981/1982) and Reimer (1984). Cadmium sulphide and cadmium selenide are important electronic semi-conductors that form the basic constituents of an efficient thin-film solar cell and are also materials for photo-phase memory effects. Although it is known that the phase of interest is the wurtzite form, there have been relatively few studies of its imperfect or defective structural lattice features. Dislocation glide in plastically deformed single crystals of 25

26

K. Kanaya, N. Baba, M. Naka, Y. Kitagawa and K. Suzuki

et a!. (1982a, 1983, 1984) applied to images from specimens prepared with the aid of an argon-ion thinning technique (Kanaya et a!., 1972) was successfully developed for the structural analysis of cadmium selenide and lattice defect image observations. Based on the quantum-mechanical approach, the time average electron density p(r) is given by the square of the wave function of a given object 2 p(r) ~i(r)~ Using this approach, the lattice images can be replaced by an integral over the continuously changing function p(r). The distribution of the electron density p(r) in an object depends on the distribution pjr) of electrons in the constituent atoms and the mutual arrangement of these atoms. The peaks of the function p(r) correspond to the centres of the atoms. If the centres of the atoms are located at points r, the electron density of such an assembly of n atoms is expressed by the continuous function —

aberrations, defocus and phase according to the equation sin(y+y0) 1 cos ;,~,= sgn[sin(y + Va)] = sin(y + = 1, for sin(y + y0) >0 (4) —

1, for sin(y + Va) <0. The diffraction spots consist of a phase band with the various shifted phases which previously demonstrated experimentally bywere Kanaya et a!. —

—

—

=

~

0, for positive contrast, sin (y + Va) >0 (5) it, for negative contrast, sin (y + ~) <0. In this procedure, the computer-generated = =

n

p(r)

(1983, 1984). In some cases, although the lattice spacing dhkl and the amplitude F(q~k,)~ remain unaltered, the processed images are displaced. To remove the distorted phases due to the disorder and lattice defects, and also astigmatic aberration, the sign of scattering phase ;kl should be synthetically corrected according to the sign of the reconstructed image contrast

p~(r ri), —

(1)

j= 1

where the electron density p(r) in a crystal or a molecule is expressed as a superposition of the electron densities of separate atoms p 3~r). According to Friedel’s law in X-ray crystallography, for a pair of spots, q,~and —qhk,, the lattice image contrast is given by the inverse Fourier transform

lattice image with an enhanced amplitude can be synthetically reconstructed. Noise removal and image enhancement

accompanied with astigmatic amplitude correction (Kanaya et a!., 1985) are considered to present more serious problems in the successful digital structural analysis from electron microscope images. Noise removal by neighbourhood 2F(q~~ averaging and gradient- and Laplacian-operator p(r) = ~ 1) (2) are conventionally used for image processing. hid Neighbourhood averaging is a straightforward where I~(qhk,)is the real part of the scattering spatial-domain technique for image smoothing. amplitude as specified by the Miller indices hkl. The procedure is to generate a smooth image The normalized amplitude f(hk!) = F~q~~J)~/ whose grey-level, at every point, is obtained by F~0,0)relative to the standard value of a central averaging the grey-level values of the pixels spot F~0,0)and its phase~ can be obtained from contained in a pre-defined neighbourhood. the algorithm of Cooley and Tukey (1965) for the The defects in lattice images are highly sensiFourier transform of lattice images. Therefore, tive to the filter window size used in the optical the phase contrast of the structure contained in reconstruction method. In digital processing, the the images can be precisely summarized from the aperture function can be used for the selection of individual harmonics a diffraction spot from the diffractogram. Ii~qh~1)Icos{2R(hu + kv + !w) + ~hki}.

(3)

From the theoretical calculation based on the Kirchhoff diffraction theory (the reader is referred to Eqns. A5 and A6 in the appendix of Kanaya et a!., 1981), ;kl can be compared with the theoretical results influenced by the phase shift parameters y and Va due to the electron lens

The function is the unity or enhancement value inside the circle and is zero outside. By multiplying the aperture function of a diffraction spot, the desired image can be extracted. The size and location of the aperture spot can be varied by monitoring on a cathode-ray tube. By using this system the effect of the aperture size of the digital filter on reconstructed lattice images was con-

Structural Analysis of Cadmium Selenide Crystals

firmed experimentally (Kanaya et a!., 1982b). When using a large aperture filter, the prominent lattice defects were clearly distinguished in images from specimens of evaporated gold crystals. During lattice defect image processing, various sizes and shapes of aperture were used for the selection of the diffraction spots involving the streaks around the computer-generated diffraction Spots. The specimen was observed to be considerably defective, and the structural details were disturbed by the dark-field contrast due to the large specimen thickness. The specimens were then prepared by the argon-ion beam thinning method in order to be thin enough to reveal the higher order diffraction spots. The sputtering removal thickness rate of CdSe using the ion beam thinning method was obtained as a function of argon- ion dose and the optimum specimen thickness, which was selected on the basis of the thickness—dose relationship. The next stage was to determine the precise location and three-dimensional arrangement of each of the atoms in the alternative hexagonal unit cell, which were obtained by the Fourier harmonic superposition method. The subsequent lattice defects ofdislocations and stacking faults which were previously reported in the publication by Suzuki et a!. (1983) were carefully processed, and the defective details in the dislocations associated with stacking faults when established by the digital processing method described above,

SPECIMEN PREPARATION BY THE ARGON-ION BEAM THINMNG PROCESS The term ‘sputtering’ refers to the ejection of atoms from the surface of a suitable target by bombardment with positively charged ions possessing energies in the range of 5—30 keV. Sputtering can be used simply to remove material from the target resulting in thinning or etching, or to deposit material from the target onto an adjacent surface as shown in Fig. 1. The sputtering apparatus we have used consists of a modified duoplasmatron source in which the ion beam is collimated and focused by an electorostatic lens onto the target. This source had a maximum brightness 2 strad1(Kanaya eta!., 1972). In fiaddition, =1011 Acm the specimens were both cooled and

27

rotated during processing in order to avoid possible artifacts and thermal damage and also a high vacuum pressure of less than 10 ~ torr was maintained by a liquid nitrogen trap. In some instances, the charged particles were filtered by a deflector (see Kanaya et a!., 1982b). Figure 1 shows the ion beam sputtering apparatus (a), in which the working chamber (b) was improved and modified to allow various operational features, including atomic shadowing (Kanaya et a!., 1974; Adachi et a!., 1976), uncoated observation and etching of biological specimens, coupled with tungsten sputter coating (Kanaya et a!., 1982), as well as thinning of solid materials (Suzuki et a!., 1982). The original cadmium selenide single crystals used for the experiments were thin ribbon crystals of about 1 mm in length and less than 1 mm in width, which were grown by the vapourtransport method. A [2110] orientation was predominantly present in the crystals. The specimens were first strained at room temperature on a tensile stage of an electron microscope, HU-500 at 350 kV, to introduce a high density of glide-dislocations. The method of straining the small thin ribbon crystals was described elsewhere (Suzuki et a!., 1981). These strained specimens were eroded to less than 10 nm thickness using the argon-ion thinning method earlier. The electron micrographs recorded at the thinning stage, together with their computergenerated diffractogramsfor CdSebombarded by argon ions of 200 ~A at 5 keY, were taken using a 125 kV Hitachi H-500H electron microscope shown in Fig. 2. The spherical and chromatic aberration coefficients are Cs = 0.7 mm and Cc=0.8 mm. The specimens were considerably distorted and the structural details in the crystallized zones were disturbed by the dark-field contrast due to the inelastic scattering. Judging from the appearance of higher order diffraction spots involving high resolution information signals in the cornputer-generated diffractograms, the required specimen thickness of less than 10 nm can be used for structural analysis at high resolution approaching the atomic level and lattice image observations showing defects. The sputtering yield S (atoms/ion) can be determined by the weight loss method for biological specimens (Kanaya et a!., 1973) or the optical interference examination method applied to thin films (Kaminsky, 1965)

28

K. Kanaya, N. Baba, M. Naka, Y. Kitagawa and K. Suzuki

a

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Specimen or substrate

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______

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For a semiconductor of CdSe, the sputtering removal rate K=4.38 (nm/mA ~min) is given by experiment, where N is the number of atoms per cm r the ion beam radius and S(v) is the sputtering yield at the incident angle v. The sputtering yield of Cd (Sm = 14.5) is very large compared with other materials (i.e. Cu, Sm = 7.0). It follows that a very critical operation is required for the small ion beam dose which is necessary in order to obtain the optimum thickness without contamination and possible artifacts. The optimum thickness required to obtain the high resolution lattice images was less than 10 nm, as supported by kinematical theory. Table 1 shows the thickness measurements compared with the extinction distance. For simplicity of calculation, a tetragonal coordinate was used.

____ ~

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______ ______ ______

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Fig. 1. The diagram illustrates the ion beam sputtering apparatus (a), together with its working chamber (b). This apparatus was used to provide specimens for high resolution electron microscopy.

It was determined that the CdSe single crystals examined constituted an alternative hexagonal phase of an imperfect wurtzite form as shown in Fig. 3, since forbidden diffraction spots in the

Legendfor page 29 Fig. 2. Electron micrographs of CdSe recorded at i25 kV with their corresponding computer-generated diffractograms. Thinning ofthe specimen by A+ ofabout 200 jiA at 5 keY: (a) thickness d = 21.3 nm for ion beam dose It= 1.5 mA~min,(b)d= 17.2, It=2.5, (c)d=15.2, It=2.9 and (d)d= 10.0, It=3.8, respectively, where the ion beam dose is shown by the integrated total dose.

Structural Analysis of Cadmium Selenide Crystals

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K. Kanaya, N. Baba, M. Naka, Y. Kitagawa and K. Suzuki

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Structural Analysis ofCadmium Selenide Crystals

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(0,0) (1,0) V .—O .37nm—. Fig. 3. The diagram shows a model wurtzite structure of CdSe as determined by the structural analysis techniques described in the text.

perfect wurtzite structure always appeared in the (2110) orientation, To determine the precise structure, the reduced specimen of less than 10 nm produced by the method of ion beam thinning was examined further by high resolution electron microscopy at 200 kV with Cs= 1.2 mm and Cc= 1.4 mm. The results are discussed below.

STRUCTURAL ANALYSIS OF CdSe SINGLE CRYSTALS Fourier harmonic superposition method If we consider the unit cell to consist of atoms, the diffraction amplitudes F(q~~,) relates to the elastic complex scattering amplitude f~(q)as a function of the generalized spatial frequency = °hkl~/(Cs/A) and the geometrical structure factor L’(hkl) of a unit cell F(q~~J) = f8(q~~I)F(hk~. (8) qhkl

For the three-dimensional case, the Fourier coefficient F(q~51)takes the form based on the diffraction theory F(q~51)= Jp(r)exp{2iri(r q~)}dv ~9) which determines the values of the scattering amplitude F(q) for an object with an electron density p(r). The reciprocal lattice vector = ~hkl

ha* + kb* + lc* is normal to the crystal lattice plane with Miller indices, and ghkj = l/dhk,, where dhkz is the spacing of these crystal phases. The characteristic diffraction angle 6h51 in the crystal is represented by the reciprocal lattice as Ohkt~~~/dhkz and ~ (10) The values of a, b and c represent the edge widths in a unit cell cube, and 2 is the wavelength of the incident beam. Thus, knowing F(q~~ 1), by calculating as above, we can construct the electron density distribution p(r) according to Eqn. (1). A densitometer was used for digitizing the transparency of the electron micrographs. The values representing the transparency on the sampling grid pointsf(s~,s~)were recorded on a magnetic disc and subsequently converted to density values by taking the logarithm. The two-dimensional Fourier transform is defined by +

F(qx~~y)=f

f

+

f(s~,s)

exp(2~ri(q~s~ + q~s~)} ds~ds~(11) in which the vector s in real space is the generalized spatial coordinates s = r~j /~/(C~2~), and the vector q in Fourier (on reciprocal) space is the generalized spatial frequency given by q = —

32

K. Kanaya, N. Baba, M. Naka, Y. Kitagawa and K. Suzuki

The functionf(s~,s ) is in turn obtained by the inverse Fourier transform (12) f(s~,s~)= F 1[(F(q)]. The normalized individual harmonics can then be obtained as phkl(r) =f(hkl)cos{22t(hu + kv) + ~hkl} (13) —

where

beam contributions from the various reflection planes (Hirsch et a!., 1965), the extinction distance dex for an unit cell volume V~is given by the equation dex = it V~/2jF(q~~,)~. (17) In the process, the thickness d of the selected area processed is theoretically given by the root of the relative intensity ratio of ~/(Ig/Io),

f(hkl) = ~1q~k

1)~/F~0, 0) ~hkl =

tan

-

~

}

(14)

in which ~hk1 is zero (positive contrast) or ~ (negative contrast) according to Eqn. (5). For a known orientation of the crystal, the individual phase of the Fourier series can easily be obtained from the results of positive or negative contrast of the lattice images, whereas the localization of lattice atoms or molecules at three-dimensional coordinates in a unit cell can be analysed from the superposition of individual harmonics in which the amplitude and its phase are accurately determined by digital processing. When determining the exact defocus value, the optical phase shift due to spherical and astigmatic aberrations and the scattering factor phase ~(0) should be taken into account y=~[q,~, +2{~cos 2~ 2}q,~j ~5(0)] —~—ö(0)/(2qe) Z //ER(1 + 2eL) 2\ ö(0) = (~)tan ‘~(O)~(0) = ~ E( 1+ ~

)~

-

(15) Here, Z is the atomic number, E the incident

d= Vc f(hkl)/2~F~q6kJ)~, where f(hkl) = ~(Ig/’o) = IF(qhk,)I/F(O, 0).

Figure 4 shows the digital processing method used for the Fourier analysis. Figure 4(a) is the original electron micrograph of a CdSe single crystal recorded at 200 kV (JEM200CX). The specimen was prepared by a method of thinning, in which a stable original structure in a (2110) orientation was predominantly observed. Figure 4(b) shows its computer-generated pattern of a Fourier transform showing diffraction spots in the (2110) plane indicated by the Miller—Bravais indices hkil. The diffraction spots obscured at low-level are enhanced. For simplicity of calculation, a transformed tetragonal coordinate is used hereafter as shown in Fig. 3. The exact value of defocus is of importance in order to achieve successful structural analysis. For this reason the micrograph was recorded at the optimum 54.8 nm undercontrast focus. of about z = 0.8,J(C~2)= As shown in Fig. 5, the condition can be obtained by the optical phase transfer function (higher order Ya is disregarded) involving the envelope function of partial coherence E(q~), it =

~

[q,~ 1 2(~+ —

energy of electrons, ER the Raydberg energy, ~ the relativistic correction factor 0.978 x 10 6 (eV 1), q~the generalized spatial frequency restricted by the screen radius of an atom and ~ and ~ are the generalized defocus 4 = z/..J(C52) and astigmatic pectively. Furthermore, aberration the amplitude ~ = N/,,/(C~2), of indiviresdual diffraction spots can be considered for higher order astigmatic defects (Kanaya et al., 1984). Then, the relative scattering amplitude f(hkl) is given by —

(18)

—

o(0)] . E(q~,)

where E(q~)= 2J1(t~)/t~, t~= 2irq~[q ~ eq], q~ —

=

6~.~/(C~/A).

5cd(0)=

(19) 0.1603,

Here, theforscattering q~=2.4 Cd, ~se(0)0hl35, factor phase q~= ~ 1.004 for Se, 2=0.00251 nm, ~/(C~23)=0.37 nm, 2itq~=0.08 are used in the calculation. The sign of the individual diffraction spots is obtained by the processing and its inverse Fourier lattice image is

f(hkl) = c~~I~(q 6~,)j/F(O, 0) cos 2~)}2). (16) According to diffraction theory and taking into account the phase difference between many =

N~/(1+ {21rq6~,(~ — ~

further confirmed. wurzite structure is givenSebyand the unit cell of twoA hexagonal close-packed Cd sublattices shifted by (1/3, 1/3, 1/8). Then the scattering amplitude of CdSe is given by

Structural Analysis of Cadmium Selenide Crystals

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Fig. 4. The images show the results from specimens ofCdSe in the (2110) orientation, whichwere recorded in the EM at 200 kV: (a) is the original micrograph, (b) its computer-generated diffractogram, (c) shows the computergenerated lattice image consisting of all the diffraction spots and (d) is its reconstructed contour-map.

2’k+l)))

+ f~d(qk~~) (exp(iit(~k+

q 3~3. The individual lattice image for a proposed model harmonic can be obtained when based on the theory of crystallography sgn[sin ycd(~)IIfcd(kiOcos(21rkv+ itiw + ~cd)] ~31i’

F( qkCl.)=fSe ( qk,I.X1+exp(iit(

~l))+ exp(i girl))

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in which the diffraction spots from the (001), (003), The(331) alternative and (3~3) hexagonal reflections structure are forbidden. model of an imperfect wurtzite form of the specimen examined is then considered from the existence of the computer-generated diffractogram consisting of the extinction diffraction spots q001, q003,

. 5)][f~~(ki1)cos(2itkv + 2itlw + ;~)] with + sgii[sin y5~( (21) fcd(kil) = 2~fCd(q~ 11)~ jcos(~itk+ ~ 1)I/FtO, 0) .

5

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f5~(kz()= 2IfSe(qkjl)~Jcos(~itk + ~irl)I/P~o, 0) ccCd=irk+ ~irl, ~se=~Ek+ ~7~ir1 (22)

34

K. Kanaya, N. Baba, M. Naka, Y. Kitagawa and K. Suzuki 1

II —

2

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__ (001)

(111) (ff2) ~0~)(ITL) (3~1) (3~3) (003) (2~0) (2~3) (2~4)(3~2l (3k) (ITO) (1T3} (2!2) (3~0) (002)

Fig. 5. The diagram shows the determination ofthe individual phase ofCdSe atoms and a defocus value from the phase transfer function.

where sgn is the sign function given by Eqn. (4), fCd(qk~l)~and f 5~(q~11)~ are the atomic scattering amplitudes, ~Cd and ~Se are the positional phases caused by the asymmetric structure, Ycd and y~ are the optical phase shifts for Cd and Se, respectively. The structural analysis data and the parameters used are given in Table 2. The thickness of CdSe studied can be measured to be about 10 nm when comparing the theoretical extinction distance. Figure 4(c) shows the computer-generated lattice images consisting of all diffraction spots and (d) is the corresponding contour map used for the determination of individual atom positions. Figure 6 shows the computer-generated lattice images: (a) consists of a set of q11 diffraction spots, (b) of a set of q111 and q2~2 diffraction spots, (c) of pair of q004 and q354 diffraction spots and (d) of pair of q001 and q003, and a set of q351 and q333 diffraction spots. The lattice images consisting of the forbidden diffraction spots shown in (d) are revealed very clearly, which allows an alternative hexagonal model satisfyingthe above analysis to be proposed and which is illustrated in Fig. 3. Since a wurtzite structure does not have a centre of symmetry and there is a polar axis parallel to [0001], the dipole moment does not balance, but creates a single polar axis. Consequently, in addition to being piezoelectric, CdSe wurtzite crystals are pyroelectric and may develop potential differences of opposite signs on

heating and cooling (Roth, 1967). Thus, an observed imperfect wurtzite structure with interlayer displacement is considered to be a result of specimen preparation. The bonding distance of CdSe was theoretically obtained to be 0.3—0.35 nm for the ionic bond, 0.26 nm for the covalent bond and 0.2 nm for the atomic bond, respectively (Vainshtein, 1981/1982). The experimental results of 0.26 nm for the columnar CdSe and 0.2,0.3 and 0.36 and0.4 nm for the displaced CdSe support the above considerations. Determination of individual atom positions and three-dimensional representations The columnar atoms shown in Fig. 3 are stable in the unit cell, but the interlayer atoms displaced from a perfect wurtzite structure are defective with considerable different phase bands as shown in Fig. 4(c) and (d). In order to distinguish the individual atoms from the molecular lattice images of a pair of CdSe, both phase and amplitude corrections due to astigmatic aberration were performed. Figure 7 shows computer-generated lattice images: (a) consists of a set of q111 and two pairs of q001 and q110 diffraction spots, (b) of sets of q111 q221, q112, q222, q113 and q2~3,and pairs of q001, q002, q003, q110 and q2~0diffraction spots, where the amplitudes of the spots are enhanced and their phases were corrected taking into consideration the sign of the phase transfer function. Figure 7(a) and (b) is in very close

Structural Analysis of Cadmium Selenide Crystals

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36

K. Kanaya, N. Baba, M. Naka, Y. Kitagawa and K. Suzuki

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~

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Fig. 6. The computer-generated lattice images: (a) consists ofa set ofq

1 1

diffraction spots, (b) a set ofq~

1and q2~2diffraction spots, (d) a pair ofq004 and q3~4diffraction spots and (d) a pair ofq001, q003 and a set ofq3~1and q333 diffraction spots.

agreement with the simulated Fourier synthetic images [Figs. 7(c) and (d)] based on Eqns. (21) and (22) with Table 2. Figure 8 shows the successful processed lattice image: (a) is the computer-generated lattice image of CdSe in the (21T0) orientation, which consists of all the diffraction spots, but the amplitudes of higher order diffraction spots are enhanced and their phases corrected according to the sign of the phase transfer function. The scattering amplitude of the Cd atom is

theoretically larger than that of the Se atom, allowing the lattice images to be clearly distinguished as shown in Fig. 8(a) and corresponding contour-map Fig. 8(b). Furthermore, the Fourier synthesis of CdSe when based on the data in Table 2 means Fig. 8(c) and (d) can be compared with Fig. 8(a) and (b~.In these synthetic lattice images, the atomic positions of CdSe were more clearly processed and in close agreement with the lattice image of the Fourier harmonic superposition method.

Structural Analysis ofCadmium Selenide Crystals

a~i1

___

37

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ck 0

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.

Fig. 7. The computer-generated lattice images from CdSe: (a) consists ofa set of q 111 and two pair of q

001 and q110diffractionspots,(b)setsofq111,q2~1,q112,q2~2,q113andq2~3andpairsofq001,q002, q003,q110andq2~0 diffraction spots, which are compared with the simulated Fourier synthetic images (c) and (d).

The precise location and three-dimensional arrangement of individual atoms in the unit cell are demonstrated in Fig. 8. The tetragonal coordinates (u, v, w) in the proposed model are: columnar Se(0, 0, 0), (1, 0, 0), (1/2, 1, 0), (.— 1/2, 1, 0), (0, 0, 1), (1, 0, 1), (1/2, 1, 1), (— 1/2, 1, 1), columnar Cd(1/2, 1/3, 1/8), displaced Se(1/3, 5/6, 7/16) and displaced Cd(O, 2/3, 5/8). Moreover, the bonding distance of Cd—Se is 0.26 nm for stable columnar atoms, and 0.2, 0.3, 0.36 and 0.4 nm for the displaced atoms.

DIGITAL STRUCTURAL ANALYSIS OF LATTICE IMAGE DEFECTS IN CdSe We have previously reported the lattice images of three types of dislocations; perfect 60°, dissociated 60°and dissociated screw dislocations, and also two types of stacking faults; intrinsic and extrinsic stacking faults (Suzuki et a!., 1982, 1983). In this paper we present the results of our experiments showing typical basal dislocations, intrinsic and extrinsic stacking faults obtained

38

K. Kanaya, N. Baba, M. Naka, Y. Kitagawa and K. Suzuki

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Fig. 8. The computer-generated lattice images of CdSe: (a) and (b) were obtained by a Fourier harmonic superposition method. These are compared with the simulated lattice images of the imperfect wurtzite model (c) and (d) processed by a Fourier synthetic method.

from electron micrographs which were recorded at 125 kV from specimens of CdSe single crystals, prepared by the method of argon-ion beam thinning. The images were extensively analysed by the digital processing method described earlier, which revealed a defective lattice arrangement based on the above precise structure of CdSe. Figure 10 shows the digital structural analysis of lattice images with a dissociated 60°partial dislocation: (a) is the original micrograph of CdSe in the (2110) orientation which was

recorded with the optimum under focus ~= 1 at 125 kV (Hitachi H-500H), (b) shows the cornputer-generated diffractogram of (a). The computer-generated lattice images consisting of all diffraction spots with the streaks around the diffraction spots are shown in Fig. 10(c) and Fig. 10(d) shows the computer-generated 60° dislocation consisting of a pair of q110 spots with streaks. The lattice images of dissociated 60°dislocations are clearly observed, and the nodes are close to the 60°orientation in Fig. 10(d), and in

Structural Analysis of Cadmium Selenide Crystals

39

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Fig. 9. The drawings show the three-dimensional arrangement ofCdSe:(a), (b), (d) face-viewof(0001) plane, first, second and third combination layers, respectively, (c) face-view of columnar Se on (b), (e) face-view of (2T10) plane and (f) side-view of unit cell assembly.

40

K. Kanaya, N. Baba, M. Naka, Y. Kitagawa and K. Suzuki

•urn~ — —

Fig. 10. A computer-generated lattice image of CdSe at (2110), (a) is the original micrograph, (b) the corresponding computer-generated diffractogram, (c) lattice image of 60° dislocation and (d) its harmonic consisting of q 1~0diffraction spots.

each boundary image at the intrinsic stacking fault the partial dislocation has g~ = 1/3 and 2/3, where b~is the partial Burgers vector in the direction of dislocation line. It can be then given

between partials D in 600 dislocation at extended nodes is related to the value of the average stacking2/24x) fault [(3 energy sin2 y4 bycthe os2 equation 4)K yD = (b 1

b~=(1/3)d110=O.125nm and (2/3)d110 —0 25 ‘23’ nm. “ ‘ Based on the anisotropic elasticity theory of dislocations (Steeds, 1973), the separation

2 4—sin2 çb)K +(3 cos 3] (24) where b is the total Burgers vector with an angle 4(60°)to the dislocation line, K1 and K3 are the material’s constants as determined by elastic constants (Gerlich, 1967). Substituting the value

.

Structural Analysis ofCadmium Selenide Crystals

41

rd~

nm

mm

Fig. 11. The computer-generated lattice images ofCdSe at (2110): (a) is the original electron micrograph, with its computer-generated diffractogram shown at (b), (c) is the lattice image of an extrinsic stacking faults, and (d) illustrates the arrangement of individual atoms.

of D = 18d110 = 6.7 nm obtained by Fig. 10(d), the intrinsic2.stacking fault energy is given by 14±5 Figure mi/rn 11 shows the digitally processed results of lattice images with the extrinsic stacking faults recorded under the same optical conditions: (a) is the original micrograph, (b) its computer-generated diffractogram, (c) the computer-generated lattice image consisting ofall the diffraction spots with streaks and (d) shows the arrangement of atoms in the lattice images with defects. The

extrinsic stacking fault (positive contrast) termmating cessed. with a Frank partial was clearly proFigure 12 shows the digitally processed results of lattice images with the interstitial loop formed on the intrinsic stacking fault: (a) is the original micrograph recorded under the same optical conditions, (b) its computer-generated diffractogram, (c) shows the lattice images consisting of all diffraction spots with streaks and (d) the arrangement of the individual atoms.

42

K. Kanaya, N. Baba, M. Naka, Y. Kitagawa and K. Suzuki

~ iiTL~J

HJ~II~ffItI~1~1 — ~,rsrrr2.nrn_~

t1fIL~I}

ljf

1 nm

~

Fig. 12. A computer-generated lattice image of CdSe at (2110): (a) is the original electron micrograph with its computer-generated diffractogram shown at (b), (c) shows a lattice image of an intrinsic stacking fault and (d) presents a diagram of the arrangement of individual atoms.

Evidence has been presented here showing that the defective structural details in dislocations and associated stacking faults can be established by the use of digital structural analytical procedures applied to specimens prepared with the aid of ion beam thinning methods. In addition, the defects were regarded as being introduced during the thinning process as aresult of damage caused by argon-ion bombardment. CONCLUSIONS (1) The digital structural analysis method

using an optical densitometer system was successfully applied to determine the isolated single atoms in the lattice images of cadmium selenide single crystals, which are prepared by the method of ion beam thinning. (2) The lattice defects of dislocations and stacking faults were established using computergenerated diffraction spots involving the streaks around the diffraction spots by various types of aperture functions. (3) It was shown that on phase determination of the Fourier harmonics for CdSe, the precise

Structural Analysis of Cadmium Selenide Crystals

phase position in addition to the optical phase, is essential. Moreover, noise extraction in the preprocessing of the digitized the electron micrographs, together with both amplitude and phase corrections due to the astigmatic aberration in a diffractogram and the subsequent image enhancement, are necessary to achieve successful structural analysis. (4) The CdSe single crystals prepared by the vapour-transport method, which were subsequently strained on a tensile stage, constitute an imperfect wurtzite phase. The tetragonal coordinates are Se(1, 0, 0), (1/3, 5/6, 7/16) and Cd(1/2, 1/3, 1/8), (0, 2/3, 5/8). Acknowledgements—The authors wish to thank Dr. T.Taoka of JEOL, for taking the high resolution micrographs at 200 kV, and Professor R. W. Home, University of East Anglia, for helpful comments and advice in connection with the preparation of the manuscript.

REFERENCES Adachi, A., Hojou, K., Katoh, M. and Kanaya, K., 1976. High resolution shadowing for electron microscopy by sputter deposition. Ultramicroscopy, 2: 17—29. Cockayne, D. J. H., Hons, A. and Spence, J. C. H., 1980. Gliding dissociated dislocations in hexagonal CdSe. Phil. Mag., 42: 773—781. Cooley, J. W. and Tukey, J. W., 1965. An algorithm for the machine calculation of complex Fourier series. Maths, Comput., 19: 297—301. Echigoya, J., Pirouz, P. and Edington, J. W., 1982. Preliminary studies of crystal defects in cadmium sulphide by highresolution transmission microscopy. Phil. Mag., A45: 455—466. Gerlich, D., 1967. The elastic constants of cadmium sulfide between 4.2—300°K.J. Phys. Chem. Solids, 28: 2575—2579. Hirsch, P., Howie, A., Nicholson, R. B., Pashley, D. W. and Whelan, M. J. (eds.), 1965. Electron Microscopy of Thin Crystals, Robert E. Krieger, Malabar. Kaminsky, M. (ed.), 1965. Atomic and Ionic Impact Phenomena on Metal Surfaces, Springer, Berlin. Kanaya, K., Koga, K. and Toki, K., 1972. Extraction ofhigh current ion beams with laminated flow. J. Phys. E: Sci. Instr., 5: 641—645. Kanaya, K., Hojou, K., Koga, K. and Toki, K., 1973. Consistent theory of sputtering of solid target by ion bombardment using power potential law. Japan J. appl. Phys., 9: 1297—1306. Kanaya, K., Hojou, K. and Adachi, K., 1974. Ion bombardment of suitable targets for atomic shadowing for high resolution electron microscopy. Micron, 5: 89—119. Kanaya, K., Baba, N. and Takamiya, K., 1981. Computeraidedreconstruction of the imagecontrast ofatom clusters from diffractograms. Micron, 12: 105—121.

43

Kanaya, K., Baba, N., Shino, M., Takamiya, K. and Oikawa, T., 1982a. Digital processing of lattice images from a diffraction spot selected in diffractograms of electron micrographs. Micron, 13: 205—219. Kanaya, K., Muranaka, Y. and Fujita, H., 1982b. Uncoated observation and etching of non-conductive materials by ion beam bombardment in scanning electron microscopy. SEM/1982/IV, SEM Inc., AMF O’Hare (Chicago), IL 60666, 1379—1394. Kanaya, K., Baba, N., Shino, M., Ichijo, T., Osumi, M. and Home, R. W., 1982c. Digital processing methods for structural analysis of an electron micrograph. SEM/1982/IV, SEM Inc., AMF O’Hare (Chicago), IL 60666, 1395—1410. Kanaya, K., Baba, N., Shinohara, C. and Osumi, M., 1983. A digital processing method for the structural analysis of lattice images ofcrystalloids obtained by electron microscopy. Micron microsc. Acta, 14: 233—247. Kanaya, K., Baba, N., Shinohara, C. and Ichijo, T., 1984. A digital Fourier harmonic superposition method for the structural analysis of human tooth enamel obtained by electron microscopy. Micron microsc. Acta, 15: 17—35. Kanaya, K., Baba, N., Kitagawa, Y. and Mukai, M., 1985. The digital structural analysis of human alveolar soft part sarcoma obtained by electron microscopy. Micron microsc. Acta, 16: 17—32. Menter, J. W., 1956. The direct study by electron microscopy of crystal lattice and imperfections. Proc. R. Soc. A236:l 19—123. Menter, J. W., 1960. Observations on crystal lattices and imperfections by transmission electron microscopy through thin films. Proc. 4th mt. Conf Electron Microsc., Springer, Berlin, 320—331. Murr, L. E. (ed.), 1970. Electron Optical Applications in Materials Science, McGraw-Hill, New York. Nonan, K. H. and Edington, J. W., 1981. A device-oriented materials study ofCdSe and Cu 2S films in solar cells. Thin Solid Films, 75: 53—65. Ray, I. M. F. and Cockayne, J. H., 1971. The dissociation of dislocations in silicon. Proc. R. Soc., A325: 543—554. Reimer, L. (ed.), 1984. Transmission Electron Microscopy, Springer Series in Optical Sciences, Vol. 36, Springer, Berlin. Roth, W. L., 1967. Crystallography. In: Physics and Chemistry of JI—VI Compounds, Aven, M. and Prener, J. S. (eds.), Ch. 3, 1—163. Skalicky, P., 1973. Computer-simulated electron micrographs of crystal defects. Phys. Stat. Sol. 20a: 1—52. Steeds, J. W. (ed.), 1973. Anisotropic Elasticity Theory of Dislocations, Clarendon Press, Oxford. Suzuki, K., Ichihara, M., Maeda, K., Takeuchi, S. and Iwanaga, H., 1981. Direct observation of partial dislocation motion in lib—VIb compounds. Phil. Mag., A43: 499—502. Suzuki, K., Takeuchi,S. and Kanaya, K., 1982. Lattice image observation of extended dislocations in CdS by high resolution electron microscopy. Jap. J. appl. Phys. Letter, 21: 621—623. Suzuki, K., Takeuchi, S., Shino, M., Kanaya, K. and Iwanaga, H., 1983. Lattice image observations ofdefects in CdS and CdSe. Trans. J. Institute Met., 24: 435—442. Vainshtein, B. K., Fridkin, V. M. and Idenbom, V. L. (eds.), 1981/1982. Modern Crystallography, I and II. Springer Series in Solid-state Physics, Vols. 15 and 21, Springer, New York.